# 2017 AMC 10B Problems/Problem 11

## Problem

At Typico High School, $60\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\%$ say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?

$\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%$

## Video Solution & Solution

~savannahsolver

The number of people who say they dislike dancing but actually like dancing is, $60%*20% = 12%$ (Error compiling LaTeX. ! Missing $inserted.) and then the number of people who say they dislike dancing and actually do dislike dancing is,$40%*90% = 36%$(Error compiling LaTeX. ! Missing$ inserted.). After this, we would want to find out what percent of the whole school says they dislike dancing but like it, so we would have $\frac{12%}{12% + 36%}$ (Error compiling LaTeX. ! File ended while scanning use of \frac .) which would then be $\frac{12%}{48%}$ (Error compiling LaTeX. ! File ended while scanning use of \frac .) which is $\frac{1}{4}$ or $\boxed{\textbf{(D)}\ 25%}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.)

## See Also

 2017 AMC 10B (Problems • Answer Key • Resources) Preceded byProblem 10 Followed byProblem 12 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.

Invalid username
Login to AoPS